80 



RECORD AND REDUCTION OF THE TIDES. 



2.00 

 .80 

 .60 



.40 

 .20 



1.00 

 .80 

 .60 

 .40 

 .20 



0.00 



0° 30 60 90 120 150 180 210 240 270 300 330 360° 



The full curves in the diagram show the form of the spring and neap tide wave 

 (the scales being arbitrary), to which has been added for convenient comparison 

 the dotted curve representing the neap tide wave on the same relative scale as the 

 spring tide wave. It is apparent that the spring tide wave is slightly steeper 

 between low and high water than between high and low water, and that the neap 

 tide wave is very nearly symmetrical in respect to rise and fall. 



AYe have seen that the duration of rise is 6 k 04 m .7, hence the duration of fall 

 will be 6 h 19. m 7; or in making ebb the time is 15 minutes greater than in making 

 flood, a circumstance in conformity with the shape of the curves of rise and fall. 

 This holds good for an average tide; according to art. (510) Tides and Waves, if 

 the place of observation is not far from the sea, or, as in our case, in a bay, the 

 water will occupy a shorter time to rise than to fall, and the inequality will be 

 greater at spring tides than at neap tides ; this is fully illustrated in the preceding 

 diagram, the spring tide wave being the steeper of the two. 



The form of the tide waves will be found closely represented by the following 

 expressions : — 



For the spring tide wave — 



5.83 + 5.58 sin. (0 + 278°) + 0.20 sin. (2 6 + 281°) ; 



For the neap tide wave — 



2.42 + 2.25 sin. (0 + 269°) + 0.09 sin. (2 6 + 290°) ; 

 in which expressions the angle 6 counts from low water to low water, from to 

 360°, and the height of the wave is expressed in feet. 



The relative numbers, given above, as the ordinates, have been changed in the 

 proportion of 2 to 11.1 for the higher and of 2 to 4.7 for the lower wave. The 

 following table shows the agreement between observation and the numerical 

 expressions, in which the 3d and higher terms are zero : — 



